But while Barth did a good job with his field goals in practice and the preseason, he lacked the kickoff distance to really challenge Carpenter.
Along with Barth, two other players were released: wide receiver Anthony Armstrong and nose tackle Louis Ellis.
Meanwhile, fullback Joe Kowalewski was waived/injured.
The four moves left the Dolphins with 66 players, which is nine below the 75-player limit each team must get down to by 4 p.m. on Tuesday.
The final roster cut to 53 is next Saturday.